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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 686 · 40 sums
TalentJR

The method (Pairs make squares): Square: n × n. Quick way: (a + b)² = a² + 2ab + b², e.g. 42² = 1600 + 160 + 4. Square root: the number that times itself gives the square; a square ending in 4 has a root ending in 2 or 8. Make a perfect square: break into primes; multiply (or divide) by the prime left without a partner. 1 + 3 + 5 + … (n odd numbers) = n². Between n² and (n + 1)² there are 2n whole numbers.

NameDateTime takenScore ___ / 40
  1. 1.What is 44²? =
  2. 2.How many whole numbers lie between 45² and 46²?
  3. 3.How many whole numbers lie between 39² and 40²?
  4. 4.Which of these is a perfect square? (a) 552 (b) 529 (c) 573
  5. 5.How many whole numbers lie between 34² and 35²?
  6. 6.A square garden has an area of 2500 square m. How long is each side (in m)?
  7. 7.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is 39²? =
  9. 9.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is √2916? =
  11. 11.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
  12. 12.How many whole numbers lie between 41² and 42²?
  13. 13.Which of these is a perfect square? (a) 1089 (b) 1127 (c) 1139
  14. 14.Which of these is a perfect square? (a) 507 (b) 484 (c) 515
  15. 15.What is the smallest whole number by which 486 must be divided to get a perfect square?
  16. 16.What is the smallest whole number by which 45 must be divided to get a perfect square?
  17. 17.A square garden has an area of 225 square m. How long is each side (in m)?
  18. 18.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is the smallest whole number by which 320 must be divided to get a perfect square?
  20. 20.What is 84²? =
  21. 21.What is √1444? =
  22. 22.What is √4225? =
  23. 23.What is √3025? =
  24. 24.How many whole numbers lie between 40² and 41²?
  25. 25.How many whole numbers lie between 9² and 10²?
  26. 26.A square garden has an area of 2209 square m. How long is each side (in m)?
  27. 27.A square garden has an area of 3364 square m. How long is each side (in m)?
  28. 28.How many whole numbers lie between 24² and 25²?
  29. 29.What is 33²? =
  30. 30.How many whole numbers lie between 15² and 16²?
  31. 31.How many whole numbers lie between 50² and 51²?
  32. 32.What is √1600? =
  33. 33.A square garden has an area of 3249 square m. How long is each side (in m)?
  34. 34.Which of these is a perfect square? (a) 786 (b) 804 (c) 784
  35. 35.What is 32²? =
  36. 36.How many whole numbers lie between 36² and 37²?
  37. 37.What is √1225? =
  38. 38.What is 83²? =
  39. 39.What is the smallest whole number by which 48 must be divided to get a perfect square?
  40. 40.A square garden has an area of 961 square m. How long is each side (in m)?

Answer key

  1. 1936
  2. 90
  3. 78
  4. 529
  5. 68
  6. 50
  7. 441
  8. 1521
  9. 529
  10. 54
  11. 2
  12. 82
  13. 1089
  14. 484
  15. 6
  16. 5
  17. 15
  18. 625
  19. 5
  20. 7056
  21. 38
  22. 65
  23. 55
  24. 80
  25. 18
  26. 47
  27. 58
  28. 48
  29. 1089
  30. 30
  31. 100
  32. 40
  33. 57
  34. 784
  35. 1024
  36. 72
  37. 35
  38. 6889
  39. 3
  40. 31

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